Partition in $\mathbb{R}^n$ with no possible refinement

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I was wondering, is it possible for a partion of a hyperrectangle $P \subset \mathbb{R}^n$ (i.e. a set of a form $P = [a_1, b_1] \times ... \times [a_n, b_n]$ to have no refinements?

If so, what is an example of such set?